Question: Simplify the following expression: $z = \dfrac{-42r + 18}{36r - 36}$ You can assume $r \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $-42r + 18 = - (2\cdot3\cdot7 \cdot r) + (2\cdot3\cdot3)$ The denominator can be factored: $36r - 36 = (2\cdot2\cdot3\cdot3 \cdot r) - (2\cdot2\cdot3\cdot3)$ The greatest common factor of all the terms is $6$ Factoring out $6$ gives us: $z = \dfrac{(6)(-7r + 3)}{(6)(6r - 6)}$ Dividing both the numerator and denominator by $6$ gives: $z = \dfrac{-7r + 3}{6r - 6}$